Question

a) In 2004 the population of City A is 2.62 million and incresing at an annual rate of 3.5% what is the expected population in 2014 let t=0 be 2004 apply the formula N=N0e^rt
b) In 2003 the population of P and A cities was 1,338,215 in 2004 the population was 1,418,041 what is the expected population in 2014 let t=0 in 2003 apply thr formulae n=n0e^rt

Answer 1

$r = 3.5/100\\\\N = N_0*e^{rt}\\\\N_0*e^0=2.62\ million,\ \ at\ t = 0\\\\N\ after\ 10\ years\\\\N=N_0*e^{(3.5/100)*10}\\\\=2.62*e^{0.35}\ million$


$N=N_0*e^{rt}\\\\ \frac{N_{2004}}{N_{2003}}=\frac{N_0*e^{r*1}}{N_0*e^{r*0}}=e^r=1418041/1338215\\\\We\ find\ r\ from\ above.\\\\ \frac{N_{2014}}{N_{2004}}=\frac{N_0*e^{r*10}}{N_0*e^{0}}=e^{10*r}\\\\N_{2014}=e^{10*3.5}*1,418,041$